System and method for identifying levels or interfaces of media in a vessel

ABSTRACT

Systems and methods for identifying the level of media in a vessel with a sensing cable including an optical fiber sensor array aligned with a heating element disposed in the vessel. An excitation source is configured to propagate at least one heat pulse through the heating element along at least a portion of the sensing cable to affect an exchange of thermal energy between the heating element and the one or more media exposed to the sensing cable. An optical signal interrogator is adapted to receive a signal from each of a plurality of sensor locations and measure a temperature profile corresponding to the heat pulse at the sensor locations. A control unit is configured to identify a level of each of media by determining properties of the media exposed to the sensing cable at each of the sensor locations based on the temperature profile corresponding thereto.

CROSS REFERENCE TO RELATED APPLICATION

This application relates and claims priority to U.S. Provisional PatentApplication No. 61/806,076, filed on Mar. 28, 2013.

FIELD

The presently disclosed subject matter relates to methods and systemsfor identifying levels or interfaces of media in a vessel. Moreparticularly, the presently disclosed subject matter relates todetermining levels and interfaces of media in a vessel using a sensingcable including an optical fiber sensor array aligned with a heatingelement.

BACKGROUND

Components of certain equipment, such as that used in the petroleum andpetrochemical industry, which includes the exploration, production,refining, manufacture, supply, transport, formulation or blending ofpetroleum, petrochemicals, or the direct compounds thereof, are oftenmonitored to maintain reliable operation. However, such components caninvolve harsh conditions, such as high temperature, high pressure,and/or a corrosive environment, making it difficult or costly to obtainreliable measurements.

Measurement of the level of, or interfaces between, one or more media ina vessel, such as a desalter unit or subsea production wellpetrochemical applications, can provide for enhanced control andoperation. For example, a desalting operation can be facilitated andenhanced by determining the location of interfaces between gas, foam,oil, emulsion, water and/or solids in a refinery desalter unit. Betteremulsion band detection and profiling can improve level, mix valve, andchemical injection control and can allow partial automation of thedesalter operation. Likewise, in connection with subsea separation ofgas, water, oil, emulsion, and sand from a well, measurement of theinterface or levels between the various media can provide enhancedcontrol of the extraction process.

Conventional approaches to measure liquid level/interface can includemonitoring locations of floated displacers, capacitance, wavereflectance, or energy absorption. However, these conventionalapproaches can suffer from certain drawbacks. For example, float-typelevel measurement is based on liquid density difference (such as betweenoil and water), and therefore it can be difficult to deploy multipledisplacers for multiple level/interface monitoring. Furthermore, themoving displacers can become coated by liquid (such as crude oil),resulting in sensor failure. Capacitance probes require direct contactwith fluids to measure electrical properties and therefore, may deliverfalse readings if fouling or waxing occurs on the probe. Additionally,because the electrical properties can be temperature dependent,capacitance-based probe techniques can also require temperaturecompensation. Wave reflectance approaches can have limited penetrationdepth because certain materials can absorb the acoustic, radiofrequency, or microwaves, and thus are unsuitable formulti-level/interface monitoring. Moreover, use of energy absorptiontechniques can be limited to narrow temperature ranges depending uponthe sensitivity of the equipment involved.

As stable desalter emulsions are becoming increasingly common due to theincrease in penetration of challenged crudes in refineries, crudes withhigh asphaltenes, high TAN, high solids, low API gravity, or highviscosity tend to form emulsions that are difficult to break. As aresult, water and salt removal can be reduced, the oil content of thebrine can increase, and disruptions in operation can become more common.Improved emulsion band detection and profiling in a desalter unittherefore would improve level, mix valve, and chemical injection controland allow for partial automation. In like manner, improved detection ofinterfaces between mixture components in subsea separation operationscan improve control over extraction.

Accordingly, there is a continued need for improved techniques foridentifying levels or interfaces of media in a vessel.

SUMMARY

The purpose and advantages of the disclosed subject matter will be setforth in and apparent from the description that follows, as well as willbe learned by practice of the disclosed subject matter. Additionaladvantages of the disclosed subject matter will be realized and attainedby the methods and systems particularly pointed out in the writtendescription and claims hereof, as well as from the appended drawings. Toachieve these and other advantages and in accordance with the purpose ofthe disclosed subject matter, as embodied and broadly described, thedisclosed subject matter includes systems and methods for identifyingthe level of one or more media in a vessel.

In accordance with one aspect of the disclosed subject matter, a methodfor identifying the level of one or more media in a vessel includesproviding within a vessel a sensing cable including an optical fibersensor array aligned with a heating element. The method includespropagating at least one heat pulse through the heating element along atleast a portion of the sensing cable to affect an exchange of thermalenergy between the heating element and the one or more media exposed tothe sensing cable. The method includes measuring, over time, atemperature profile of the sensing cable corresponding to the heat pulseat each of a plurality of sensor locations on the optical fiber sensorarray. The method includes identifying a level of each of the one ormore media by determining one or more properties of the one or moremedia exposed to the sensing cable at each of the plurality of sensorlocations based on the temperature profile corresponding thereto.

In certain embodiments, the vessel can include a desalter unit andidentifying the level of one or more media can include identifying thelevel of one or more of gas, foam, oil, emulsion, water, or solids.Alternatively, the vessel can include a subsea production well, andidentifying the level of one or more media can include identifying thelevel of one or more of gas, foam, crude, water, emulsion, or sand.

As embodied herein, the at least one heat pulse can include a pluralityof heat pulses. Measuring the temperature profile corresponding to theheat pulse at each of the plurality of sensor locations can include, foreach sensor location, measuring a plurality of temperatures over aperiod of time upon arrival of the heat pulse at the sensor location.Identifying the level of the one or more media can include, for eachtemperature profile, performing a regression of the plurality oftemperatures over a logarithm of corresponding measurement times for apredetermined time window in the period of time to generate a slope andan intercept of the regression, wherein the slope and the interceptrelate to the one or more properties of the medium exposed to thesensing cable at the sensor location. Identifying the level of the oneor more media can include calculating a difference in the slope and theintercept between adjacent sensor locations, wherein the differenceindicates an interface between two of the one or more media if thedifference exceeds a predetermined threshold. Additionally oralternatively, identifying the level of the one or more media caninclude, for each temperature profile, generating a time derivative bycalculating a derivative of the plurality of temperature measurementswith respect to time, applying a transform to the time derivative togenerate a complex spectrum, and determining an amplitude and a phase ofthe complex spectrum, wherein the amplitude and the phase of the complexspectrum relate to the one or more properties of the medium exposed tothe sensing cable at the sensor location. Identifying the level of theone or more media can further include generating a frequency derivativespectrum by calculating the derivative of the complex spectrum withrespect to frequency and determining an amplitude and a phase of thefrequency derivative spectrum, wherein the amplitude and the phase ofthe frequency derivative spectrum relate to the one or more propertiesof the medium exposed to the sensing cable at the sensor location.Identifying the level of the one or more media can include calculating adifference in the amplitude and the phase between adjacent sensorlocations, wherein the difference indicates an interface between two ofthe one or more media if the difference exceeds a predeterminedthreshold.

In accordance with another aspect of the disclosed subject matter, asystem for identifying the level of one or more media in a vesselincluding one or more media includes a sensing cable including anoptical fiber sensor array aligned with a heating element disposed inthe vessel, the optical fiber sensor array having a plurality of sensorlocations. The system includes an excitation source coupled with theheating element and configured to propagate at least one heat pulsethrough the heating element along at least a portion of the sensingcable to affect an exchange of thermal energy between the heatingelement and the one or more media exposed to the sensing cable. Thesystem includes an optical signal interrogator coupled with the opticalfiber sensor array and adapted to receive a signal from each of theplurality of sensor locations and configured to measure, over time, atemperature profile of the sensing cable corresponding to the heat pulseat each of the plurality of sensor locations on the optical fiber sensorarray. The system includes a control unit, coupled with the heatingelement the optical signal interrogator, to identify a level of each ofthe one or more media by determining one or more properties of the oneor more media exposed to the sensing cable at each of the plurality ofsensor locations based on the temperature profile corresponding thereto.

In certain embodiments, the vessel can include a desalter unit, and theone or more media can include one or more of gas, foam, oil, emulsion,water, or solids. Alternatively, the vessel can include a subseaproduction well, and the one or more media can include one or more ofgas, foam, crude, water, emulsion, or sand.

As embodied herein, the optical signal interrogator can be configured,for each of the plurality of sensor locations, to measure a plurality oftemperatures over a period of time upon arrival of the heat pulse at thesensor location. The control unit can be configured, for eachtemperature profile, to perform a regression of the plurality oftemperatures over a logarithm of corresponding measurement times for apredetermined time window in the period of time to generate a slope andan intercept of the regression, wherein the slope and the interceptrelate to the one or more properties of the medium exposed to thesensing cable at the sensor location. The control unit can be configuredto calculate a difference in the slope and the intercept betweenadjacent sensor locations, wherein the difference indicates an interfacebetween two of the one or more media if the difference exceeds apredetermined threshold. Additionally or alternatively, the control unitcan be configured, for each temperature profile, to generate a timederivative by calculating a derivative of the plurality of temperaturemeasurements with respect to time, apply a transform to the timederivative to generate a complex spectrum, and determine an amplitudeand a phase of the complex spectrum, wherein the amplitude and the phaseof the complex spectrum relate to the one or more properties of themedium exposed to the sensing cable at the sensor location. The controlunit can be further configured to generate a frequency derivativespectrum by calculating the derivative of the complex spectrum withrespect to frequency, and determine an amplitude and a phase of thefrequency derivative spectrum, wherein the amplitude and the phase ofthe frequency derivative spectrum relate to the one or more propertiesof the medium exposed to the sensing cable at the sensor location. Thecontrol unit can be configured calculate a difference in the amplitudeand the phase between adjacent sensor locations, wherein the differenceindicates an interface between two of the one or more media if thedifference exceeds a predetermined threshold.

It is to be understood that both the foregoing general description andthe following detailed description are exemplary and are intended toprovide further explanation of the disclosed subject matter claimed.

The accompanying drawings, which are incorporated in and constitute partof this specification, are included to illustrate and provide a furtherunderstanding of the disclosed subject matter. Together with thedescription, the drawings serve to explain the principles of thedisclosed subject matter.

BRIEF DESCRIPTION OF THE DRAWINGS

The patent or application file contains at least one drawing executed incolor. Copies of this patent or patent application publication withcolor drawing(s) will be provided by the Office upon request and paymentof the necessary fee.

FIG. 1A is a schematic diagram of an exemplary sensing system inaccordance with the disclosed subject matter.

FIG. 1B is a cross sectional view of an exemplary sensing cableconfiguration in accordance with the disclosed subject matter.

FIG. 1C is a cross sectional view of another exemplary sensing cableconfiguration in accordance with the disclosed subject matter.

FIG. 2 depicts a representative plot of current and heat pulses andcorresponding temperature response in accordance with the disclosedsubject matter.

FIG. 3 is a graph illustrating a direct temperature sensing techniquefor a plurality of sensor locations in accordance with the disclosedsubject matter.

FIG. 4A is a graph illustrating log-time regression sensing technique inaccordance with the disclosed subject matter.

FIG. 4B is a graph illustrating log-time regression sensing techniquefor a plurality of sensor locations in accordance with the disclosedsubject matter.

FIG. 5A is a graph illustrating thermal excitation energy concentrationat harmonics and fundamental frequencies of heat pulses in connectionwith a frequency spectrum sensing technique.

FIG. 5B is a graph illustrating the phase of a frequency-derivativespectrum in connection with frequency spectrum sensing techniques over aplurality of sensor locations in accordance with the disclosed subjectmatter.

FIG. 5C is a graph illustrating the amplitude of a frequency-derivativespectrum in connection with frequency spectrum sensing techniques over aplurality of sensor locations in accordance with the disclosed subjectmatter.

FIG. 6 is a schematic representation of a system and method foridentifying the level and interfaces of media in a vessel in accordancewith an exemplary embodiment of the disclosed subject matter.

FIG. 7 is a schematic cross sectional view of a representativeembodiment of a shield for a cable configuration in accordance with anexemplary embodiment of the disclosed subject matter.

DETAILED DESCRIPTION

As noted above and in accordance with one aspect of the disclosedsubject matter, methods disclosed herein include identifying the levelof one or more media in a vessel with a sensing cable including anoptical fiber sensor array aligned with a heating/cooling elementincludes propagating at least one heating/cooling pulse through theheating/cooling element along at least a portion of the sensing cable toaffect an exchange of thermal energy between the heating element and oneor more media exposed to the sensing cable. The method includesmeasuring, over time, a temperature profile of the sensing cablecorresponding to the heat pulse at each of a plurality of sensorlocations on an optical fiber sensor array. The method includesidentifying a level of each of the one or more media by determining oneor more properties of the one or more media exposed to the sensing cableat each of the plurality of sensor locations based on the temperatureprofile corresponding thereto.

Furthermore, systems for identifying the level of one or more media in avessel are also provided. Such systems include one or more mediaincludes a sensing cable including an optical fiber sensor array alignedwith a heating element disposed in the vessel, the optical fiber sensorarray having a plurality of sensor locations. The system furtherincludes an excitation source coupled with the heating element andconfigured to propagate at least one heat pulse through the heatingelement along at least a portion of the sensing cable to affect anexchange of thermal energy between the heating element and the one ormore media exposed to the sensing cable. The system also includes anoptical signal interrogator coupled with the optical fiber sensor arrayand adapted to receive a signal from each of the plurality of sensorlocations and configured to measure, over time, a temperature profile ofthe sensing cable corresponding to the heat pulse at each of theplurality of sensor locations on the optical fiber sensor array. Acontrol unit, coupled with the heating element and the optical signalinterrogator, identifies a level of each of the one or more media bydetermining one or more properties of the one or more media exposed tothe sensing cable at each of the plurality of sensor locations based onthe temperature profile corresponding thereto.

Reference will now be made in detail to the various exemplaryembodiments of the disclosed subject matter, exemplary embodiments ofwhich are illustrated in the accompanying drawings. The accompanyingfigures, where like reference numerals refer to identical orfunctionally similar elements, serve to further illustrate variousembodiments and to explain various principles and advantages all inaccordance with the disclosed subject matter. The accompanying figures,where like reference numerals refer to identical or functionally similarelements, serve to further illustrate various embodiments and to explainvarious principles and advantages all in accordance with the disclosedsubject matter. For purpose of explanation and illustration, and notlimitation, exemplary embodiments of the disclosed subject matter areshown in FIGS. 1-7.

In accordance with the disclosed subject matter, characteristics of oneor more materials can be measured with the use of an optical fibersensor array having a plurality of sensor locations aligned with aheating/cooling element in a sensing cable. At least one heating/coolingpulse is propagated through the heating/cooling element along at least aportion of the sensing cable to affect an exchange of thermal energybetween the heating/cooling element and one or more media exposed to thesensing cable. A temperature profile of the sensing cable (e.g., in thetime domain and/or spatial domain) corresponding to the heating/coolingpulse at the plurality of sensor locations on the optical fiber sensorarray can be measured to support a variety of techniques in accordancewith the disclosed subject matter.

Generally, for purpose of illustration and not limitation, thermalproperties, such as material density, thermal conductivity, heatcapacity, or heat diffusion coefficient, of one or more materials can bemeasured by generating a heat disturbance and sensing a temperatureresponse. In like fashion, dynamic physical properties, such as the flowof a material, can also be measured. As disclosed herein, techniques formeasuring temperature can include obtaining temperature measurements inboth the temporal and spatial domain. For example, distributedtemperature sensing (DTS) systems can provide temperature measurementsalong the length of a sensing cable continuously or at regularintervals. The change in these temperature measurements can correspondto certain properties of a surrounding material or materials.

For purpose of illustration, and not limitation, an exemplary system formeasuring the characteristics of a material in accordance with anexemplary embodiment of the disclosed subject matter will be described.In general, with reference to FIG. 1A, an exemplary sensing system inaccordance with the disclosed subject matter can include a sensing cable101 having disposed therein a heating/cooling device 103 and opticalfiber sensor array having a plurality of sensors 102. The sensing cable101 can be operatively coupled with a control unit 106. For example, theheating/cooling device 103 can be coupled with an excitation source 105,which in turn can be coupled with the control unit 106. Likewise, theoptical fiber sensor array 102 can be coupled with a signal interrogator104, which can be coupled with the control unit 106. Generally, uniformheat can be delivered (e.g., heat energy can be provided or absorbed)along the sensing cable 101 via the heating/cooling device 103 and theexcitation source 105. A temperature profile or its variation with time(e.g., variation rate) can be measured using the optical fiber sensorarray 102 and signal interrogator 104. The control unit 106 can beadapted to collect data, process data, and/or present data forvisualization, for example via one or more displays (not shown).

The sensing cable 101 can be arranged in a variety of configurations.Two exemplary configurations are depicted in FIG. 1B and FIG. 1C,respectively. For example, FIG. 1B depicts a cross section of a sensingcable 101 with the heating/cooling device 103 and the optical fibersensor array 102 arranged in parallel with each other. The sensing cable101 can include, for example, an outer casing (not shown) optionallyfilled with a filler material 110 to maintain the heating/cooling device103 and optical fiber sensor array 102 in place. Additionally oralternatively, the filler can be extended about the heating/coolingdevice 103 and temperature sensor 102 with or without the outer casing.The filler can be, for example, a material with high thermalconductivity, such as magnesium oxide (MgO). The outer casing can be arigid and/or durable material, for example a metal tube. To ensuremeasurement accuracy, e.g., under harsh conditions, such as fouling orcorrosion, the sensing cable 101 casing can be treated with a suitablecoating, as described in more detail below. Alternatively, and asdepicted in cross section in FIG. 1C, the heating/cooling device 103 andthe temperature sensor array 102 can be generally coaxial with eachother, wherein the heating/cooling device 103 is disposed concentricallyaround the temperature sensor array 102.

As embodied herein, the sensing cable 101 can be mineral insulated forprotection of a optical fiber sensor array 102 including one or moreoptical fibers. The optical fibers can be coated and placed into aprotective tube structure for enhanced mechanical integrity andresistance to adversary effects of environmental factors, such as H₂,H₂S and moisture. The sensing cable 101 can further be protected usingmetal and mineral insulation material (e.g., MgO) for effective thermalconduction. The optical fibers can have a relatively small diameter, andthus can be placed into a protective tube with a relatively smalldiameter, allowing a faster thermal response and dynamic processmonitoring. One of ordinary skill in the art will appreciate that thedimensions of the sensing cable 101 can be selected for a desiredapplication. For example, if further protection from the localenvironment is desired, a sensing cable 101 with a larger diameter, andthus additional filler, can be selected.

Furthermore, a number of commercially available fibers for thetemperature sensor 102 can be used, such as a Fiber Bragg Grating array,Raman scattering based sensor, Rayleigh scattering based sensor orBrillioun scattering based sensor. One of ordinary skill in the art willappreciate that each type of fiber sensor can have certain properties,such as response time, sensing resolution, immunity to hydrogendarkening, effective sensing cable length, and ability to sensetemperature and/or strain, as illustrated for purpose of example and notlimitation in Table 1. For example, a Fiber Bragg grating sensing systemcan include a relatively fast response time, high spatial resolution,and can be employed over a sensing cable length upwards of 100 km orlonger in connection with the use of optical fiber amplifiers. Raman andBrillouin scattering sensing systems can have relatively low responsetimes (e.g., on the order of several seconds), and spatial resolution onthe order of centimeters. Rayleigh scattering sensing systems, whenoperated to sense temperature, can have a response time of severalseconds with relatively high spatial resolution.

TABLE 1 Fastest Typical point Immunity Longest response sensor to H2sensor Sensor types time size (m) darkening cable length Fiber Bragg <10ms 0.01 high <100 km or Grating (FBG) longer Raman >Several 0.25~0.5 low <100 km scattering sensor seconds Rayleigh >Several 0.01 low  <70 mscattering sensor seconds (Temp) Rayleigh  <1 ms 0.5  low <100 kmscattering sensor (Acoustic) Brillouin >Several 0.1~50 low <100 kmscattering sensor seconds

One of ordinary skill in the art will also appreciate that certain ofthe various types of sensing systems can be used to sense temperatureand/or strain (e.g., to sense acoustics). For example, Fiber BraggGrating sensing systems can be used to measure both temperature andstrain, for purposes of sensing temperature and acoustics. Ramanscattering sensing systems are typically used to sense temperature.Brillouin scattering sensing systems can be used to measure temperatureand strain, and are typically used to sense temperature. Rayleighscattering sensing systems can be used to measure temperature andstrain, and can be used to sense either temperature or acoustics. One ofordinary skill in the art will appreciate that when Rayleigh scatteringsensing systems are used to sense acoustics, response time can increaseto lower than 1 ms and spatial resolution can increase to approximately50 cm.

Referring again to FIG. 1A, and as noted above, the control unit 106 canbe coupled with the signal interrogator 104. The signal interrogator 104can be, for example, an optical signal interrogator. Various opticalsignal interrogators may be used, depending on the type of optical fibersensing techniques to be employed. The controller 106 can be adapted toperform signal processing on real-time temperature data provided by thesignal interrogator 104. For example, the control unit 106 can beadapted to identify and record continuous or repeated temperaturemeasurements at each of a plurality of sensor locations along thesensing cable 101. Additionally, the control unit 106 can be adapted toprocess temperature measurements over time to identify a characteristicof the material surrounding the sensing cable at one or more sensorlocations.

As disclosed herein, a variety of suitable methods can be employed forgenerating the heating/cooling pulse along the sensing cable 101. Asused herein, the term “pulse” includes a waveform of suitable shape,duration, periodicity, and/or phase for the intended purpose. Forexample, and not limitation, and as described further below, the pulsemay have a greater duration for one intended use, such as thedetermination of deposits, and a shorter duration for another intendeduse, such as the determination of flow. As embodied herein, theheating/cooling device 103 can be an electrically actuated device. Forexample, the heating/cooling device 103 can include a resistive heatingwire, and the excitation source 105 can be electrically coupled with theheating wire and adapted to provide a current there through. Passing ofa current through the resistive heating wire can provide thermal energyalong the length of the sensing cable 101, thereby generating a uniformheating/cooling effect along the sensing cable. Alternatively, theheating/cooling device 103 can include a thermoelectric device, and canbe likewise coupled to the excitation source 105. The thermoelectricdevice can use the Peltier effect to heat or cool a surrounding medium.That is, for example, the thermoelectric device can be a solid-stateheat pump that transfers heat from one side of the device to the other.The thermoelectric device can be configured, for example, to provideheating to the optical fiber sensor for a certain polarity of electricpotential and cooling for the opposite polarity. As disclosed herein,and for purpose of simplicity, the terms “heating/cooling device”, and“heating/cooling pulse” will be referred to generally as a “heatingdevice” or “heating element” and as a “heat pulse,” respectively.Depending upon the context, such terms are therefore understood toprovide heating, cooling, or both heating and cooling.

In an exemplary embodiment of the disclosed subject matter, theexcitation source 105 can be configured to deliver current in apredetermined manner. For example, the excitation source 105 can beconfigured to generate pulses having predetermined wave forms, such assquare waves, sinusoidal waves, or saw tooth waves. The excitationsource 105 can be configured to generate the pulses at a predeterminedfrequency. For example, and not limitation, and with reference to FIG.2, the excitation source 105 can be configured to generate an electricpulse of a rectangular wave form 210 through the heating/cooling element103. The electric pulse can create a heat pulse 220 in theheating/cooling element 103 with the same wave form. That is, forexample, the heat flow through the heating/cooling element 103 can begiven by I²R/A, where I is the current, R is the resistance of theheating/cooling element 103, and A is the surface area of a crosssection of the heating/cooling element 103. The heat pulse can result ina heat exchange between the sensing cable 101 and the surrounding media.The temperature at each sensor location can be recorded to generate a“temperature profile” 230 for each sensor location. For example, thetemperature at each sensor location can be recorded with a samplingfrequency of 50 Hz. The temperature profile 230 can correspond tocharacteristics of the medium surrounding the sensing cable 101 at eachsensor location.

For purposes of illustration, and not limitation, the underlyingprinciples of thermally activated (“TA”) measurement techniques will bedescribed generally. Prior to heating or cooling by the heating/coolingdevice 103, temperature measurements of the surrounding medium can betaken with the optical fiber sensor array 102 of the sensing cable 101and the temperature profile can be recorded as a reference. Due to theJoule effect, the heating device 103 can deliver a constant and uniformheat along the cable, heating up both cable and surrounding medium nearthe cable surface. For purposes of illustration, the temperaturemeasured by the optical fiber can be described by the followingequation:

$\begin{matrix}{{\frac{\partial T}{\partial t} = {\frac{1}{{mc}_{p}}\left( {{\overset{.}{E}}_{gen} - {\overset{.}{E}}_{loss}} \right)}},} & (1)\end{matrix}$

where Ė_(gen) is the heat generation rate per unit length from theheating device, Ė_(loss) is the heat loss rate due to heat transfer fromthe sensing cable to the surrounding medium, and m and c_(p) representthe mass and heat capacitance of the sensing cable per unit length. Theheat generation within the sensing cable due to the Joule effect can begiven by:

Ė _(gen) ∝Z _(i) ²,  (2)

where Z is the impedance of the sensing cable per unit length and therate of heat loss from the sensing cable to the surrounding media can bedecomposed into heat diffusion and heat convection (e.g., Ė_(loss) caninclude both heat diffusion (conduction) in a stationary medium and orconvective heat transfer in a flowing medium):

Ė _(loss) =Ė _(diffusion) +Ė _(convection)  (3)

For a stationary medium, the heat loss term can be given as:

Ė _(loss) ∝AkΔT,  (4)

where A is effective heat transfer area of the sensing cable, k iseffective heat conduction coefficient of the medium and ΔT is theeffective temperature gradient across the sensing cable and the medium.

The heat capacitance of the cable per unit length can limit thefrequency of the thermal response of the cable, and thus the cable canbe designed with a heat capacitance suited to the desired datafrequency. Because heat generation can be relatively constant anduniform, the rate of change in localized temperature can dependprimarily on the heat transfer between the cable and the surroundingmedium. If the localized heat transfer is high at a particular point onthe sensing cable, then the rate of change of temperature at that pointalong the cable, measured by one temperature sensor in the opticalfiber, can be small. Otherwise, the temperature changing rate will belarge. When subject to a heterogeneous medium or a mixed mediumconsisting of layers of different fluids or the like, the spatialdistribution of the temperature along the sensor array can be indicativeof the interface between the different media.

For purpose of illustration, and not limitation, transient temperatureanalysis techniques to determine characteristics of a medium will now bedescribed with the sensing cable modeled as an infinitely long thincylinder placed in an infinite homogeneous medium. For purposes of thisdescription, it is assumed that at time zero (t=0) an electricalcurrent, i, and the heat generation rate per length of the cylinder isgiven by:

q=πr ₀ ² z ₀ i ²,  (5)

where r₀ is the radius of the cylinder, and z₀ is the resistance of thecylinder per unit of volume. A closed form solution for the temperatureon the surface of the cylinder can be given as:

$\begin{matrix}{{{{T\left( {r_{0},t} \right)} - T_{\infty}} = {\frac{q}{4\; \pi \; k}{\int_{\frac{r_{0}^{2}}{4\; \alpha \; t}}^{\infty}{\frac{^{- u}}{u}\ {u}}}}},} & (6)\end{matrix}$

where k and α are the heat conductivity and diffusivity coefficients ofthe medium, and T_(∞) is the initial temperature distribution along thesensing cable. The normalized temperature change and normalized time tcan be defined as:

$\begin{matrix}{{{\Delta \; T^{*}} = \frac{{T\left( {r_{0},t} \right)} - T_{\infty}}{q/\left( {4\; \pi \; k} \right)}}{and}} & (7) \\{t^{*} = {\frac{4\; \alpha \; t}{r_{0}^{2}}.}} & (8)\end{matrix}$

Equation 6 can thus be given as:

$\begin{matrix}{{\Delta \; T^{*}} = {\int_{1/t^{*}}^{\infty}{\frac{^{- u}}{u}\ {{u}.}}}} & (9)\end{matrix}$

The incomplete gamma function can have following expansion form forsmall but non-zero value of z (0<z<2.5):

$\begin{matrix}{{\Gamma (z)} = {{\int_{z}^{\infty}{\frac{^{- u}}{u}\ {u}}} = {{- \gamma} - {\ln (z)} - {\sum\limits_{n = 1}^{\infty}\; {\frac{\left( {- z} \right)^{n}}{n\left( {n!} \right)}.}}}}} & (10)\end{matrix}$

The temperature response as given by equation 6 above can be furtherapproximated as

ΔT*≈−γ−ln(1/t*),  (11)

when

z=1/t*<<1.  (12)

In accordance with this illustrative and non-limiting model, comparisonof the normalized temperature change as a function of normalized time(e.g., as given by equation 9 and equation 11, respectively) indicatesthat when the normalized time is greater than approximately 10, equation11 is a good approximation of normalized temperature change. Moreover,equation 11 above indicates that temperature change can increaselinearly with the log of time when the heating time is sufficientlylarge so as to satisfy the criteria in equation 12. Thus, the equationcan be written as:

ΔT(r ₀ ,t)≈a+b ln(t),  (13)

where parameters a and b are function of thermal properties of themedium for given heating rate, and are given by:

$\begin{matrix}{{a = {\frac{q}{4\; \pi \; k}\left( {{- \gamma} - {\ln \left( \frac{r_{0}^{2}}{4\; \alpha} \right)}} \right)}}{and}} & (14) \\{b = {\frac{q}{4\; \pi \; k}.}} & (15)\end{matrix}$

Thus, equation 13 can provide a theoretical basis for determining thethermal properties of a medium based on measurement of transienttemperature. One of ordinary skill in the art will appreciate thatcontinuous heating can consume more electrical energy and makemeasurements less sensitive to dynamic change of the thermal propertiesto be measured (e.g., when the medium mixture changes with time), andthus pulsed heating in accordance with the disclosed subject matter canprovide benefits such as decreased electrical energy usage and formeasurement of dynamic conditions of surrounding materials.

For purpose of illustration, and not limitation, an exemplary method ofmeasuring the characteristics of the media surrounding the sensing cableusing thermal analysis sensing techniques will be described. In general,an optimized waveform of electrical pulse (for example, a square wave)can be delivered along the length of the heating/cooling device 103, andtemperature can be monitored using a temperature sensor array 102, e.g.,optical fiber sensors. Owing to the uniformity of the heating/coolingeffect along the sensing cable, temperature readings can vary dependingon localized heat transfer process, which can be a function of thethermal properties (e.g., thermal conductivity, heat capacity) andphysical conditions (static or flow) of the medium surrounding thesensing cable 101. The control unit 106 can be adapted to determine thecharacteristics of the surrounding media simultaneously, using thetemperature profile.

A single heating pulse (e.g., arising from an optimized waveform ofelectrical pulse) can create a temperature response which can be derivedin accordance with the exemplary and non-limiting model described hereinusing superposition as follows:

$\begin{matrix}{{{T\left( {r_{0},t} \right)} - T_{\infty}} = {\frac{q}{4\pi \; k}{\left( {{\int_{\frac{r_{0}^{2}}{4\alpha \; t}}^{\infty}{\frac{^{- u}}{u}\ {u}}} - {\int_{\frac{r_{0}^{2}}{4{\alpha {({t - t_{0}})}}}}^{\infty}{\frac{^{- u}}{u}\ {u}}}} \right).}}} & (16)\end{matrix}$

The first term in the bracket of equation 16 can represent the heatingfrom t to t₀, and the 2nd term the cooling after t₀. Data collectedduring heating and cooling are analyzed separately, as disclosed herein,to derivate estimates of thermal properties of the medium.

Based upon the above, the control unit 106 can be adapted to determinethe characteristics of the surrounding media using a variety of suitabletechniques. For example, the temperature profile at each sensor locationcan be used to determine the characteristics of the surrounding mediadirectly. The temperature measurements during heating and/or cooling ofthe sensing cable, corresponding to the timing of the rectangularelectrical pulse, can be used to generate a feature-temperature profileat each sensor location. For example, the feature-temperature profilescan be extracted from the temperature data at distinctive conditions:heating (e.g., the condition during which the heat pulse is passing overa sensor location), cooling (e.g., the condition during which the heatpulse has passed over the sensor location and heat is being exchangedbetween the sensing cable and the surrounding media) and peaktemperature (e.g., approximately the maximum temperature recorded at thesensor location for each heat pulse).

For purpose of illustration, and not limitation, and with reference toFIG. 3, the control unit 106 can be configured to determine temperaturecharacteristics of surrounding media using the feature-temperatureprofile at each sensor location. FIG. 3 shows distribution of featuretemperatures along a sensing cable exposed to different media atdifferent sensor locations. Graph 330 depicts the measured temperatureprofiles for a plurality of sensor locations. In accordance with thedisclosed subject matter, feature-temperatures 331 b, 332 b, and 333 bcan be extracted from the measured temperature profile depicted in graph330. For example, at each sensor location, feature-temperature 331 b cancorrespond to a heating condition (e.g., while the heat pulse is passingover the sensor location), and can be extracted for each sensor locationat a corresponding time 331 a. Likewise, feature-temperature 332 b cancorrespond to a peak temperature, and can be extracted for each sensorlocation at a corresponding time 332 a. Similarly, feature temperature333 b can correspond to a cooling condition (e.g., after the heat pulsehas passed over the sensor location and during which heat exchangebetween the cable and the surrounding media takes place) and can beextracted for each sensor location at a corresponding time 333 a.Temperature 310 is the measured temperature at each sensor locationduring ambient conditions (e.g., no heat is applied).

As illustrated by FIG. 3, the feature temperature at each sensorlocation can correspond to the temperature characteristics of thesurrounding media. For example, as depicted in FIG. 3, a 36 inch sensingcable arranged in a vertical configuration with a sensor disposed orlocated each unit inch along the cable can be exposed to a stack of air,oil, emulsion, and water. It should be noted that FIG. 3 depicts datafrom 24 sensor locations. Assuming each medium is stationary around thesensing cable, the rate of heat exchange, and thus thefeature-temperature profiles 331 b, 332 b, and 333 b, between thesensing cable and the surrounding media at each sensor location cancorrespond to the heat conduction of the surrounding media. That is, forexample, heat transfer between the sensing cable and surrounding air canbe lower than that between the sensing cable and water, as water has ahigher heat conduction. Oil and emulsion layers can also be identifiedin this manner.

The determination of the characteristics of the media surrounding thesensing cable can be achieved by further configuring the control unit106 to process the temperature profile. For example, in accordance withan exemplary embodiment of the disclosed subject matter, the regressionof the temperature over log of time can be performed over an interval oftime corresponding to each heat pulse for each sensor location. Theslope and intercept of the regression can be used to identify thematerial characteristics. For example, the regression can take thefunctional form of T=b+m ln(t), where T is the temperature measurement,ln(t) is the natural log of the time of the temperature measurement, bis the intercept of the regression, and m is the regression coefficient.

The interval over which the regression is taken can be, for example,during the heating condition described above (e.g., during which theheat pulse passes over the sensor location). Because heating can occurin a logarithmic manner, taking the regression as a function of the logof time and provide for results with lower error (e.g., a highercorrelation coefficient). That is, for example, the temperature as afunction of the log of time can be substantially linear over the heatingperiod. Alternatively, the interval over which the regression is takencan be during the cooling condition described above. For purpose ofillustration, and not limitation, for a square electrical pulse from 0current to a constant non-zero value, the constant non-zero currentvalue can correspond to the heating stage, and zero current cancorrespond to the cooling stage. The slope of the regression for theheating stage can be computed over a fraction of pulse duration when thecurrent is non-zero, while slope of the regression for the cooling stagecan be computed over a fraction of the time for which the currentchanges to zero value. Additionally or alternatively, the regression cantake a number of suitable functional forms. For example, an nth orderpolynomial regression can be taken if the functional form of thetemperature profile resembles an nth order polynomial.

For purpose of illustration, FIG. 4A shows the regression results of onetemperature measurement at a sensor location in each material of FIG. 3.Line 420 corresponds to a plot of temperature at a sensor location inoil over the log of time. Likewise, lines 430, 440 and 450 correspond toa plot of temperature at a sensor location in air, emulsion, and water,respectively, over the log of time. Regression can be performed over aregression interval 410, which can correspond to the heating conditionof the respective temperature sensor. The results of the regression canbe plotted. For example, line 421 is a plot of the regression of line420. As illustrated by FIG. 4A, the slope and intercept of eachregression can correspond to a characteristic of the surroundingmaterial, and such characteristics can be determined. That is, withreference to FIG. 4A, each material having different thermalcharacteristics can have a different slope and intercept, and can thusbe identified. As depicted in FIG. 4A, The deviations in measurementsresulting from the linear fitting line after the regression interval, asshown by line 420 and line 421, can be due to boundary effects from thewall of the vessel. One of ordinary skill in the art will appreciatethat the description of the underlying principles herein assumes thethermal energy delivered by the sensing cable diffuses out without anyboundaries. However, in the presence of such boundaries, thermal energywill be contained in a finite space and eventually thermal equilibriumwill be reached. Accordingly, the regression interval can be selectedbased on a desired application, including corresponding boundaryconditions.

For purpose of illustration. FIG. 4B shows the regression results for 24temperature sensors of FIG. 3, showing both slopes 450 and intercepts470. As illustrated by FIG. 4A and FIG. 4B, in certain circumstancesthese techniques can provide determination of material characteristicswith reduced error, comparing results from FIG. 4B with FIG. 3 todifferentiate the emulsion layer and the oil layer. The interval overwhich the regression can be performed can be predetermined to reduceboundary effect errors (e.g., error 422 induced by boundary effects inthe plot of line 420). That is, for example, taking the regression overa small interval can omit certain features of a temperature profile thatcan correspond to a particular characteristic. Accordingly, theregression interval can be predetermined such that errors induced byboundary effects are reduced. For example, the regression interval canbe predetermined by calibration and/or with reference to knownparameters or operating conditions of the system, such as expectedfeatures of a temperature profile.

In accordance with another aspect of the disclosed subject matter,enhanced determination of the characteristics of media surrounding thesensing cable can be achieved with a control unit 106 configured toprocess the temperature profile in the frequency domain. A N-pulse train(i.e., application of a certain periodic form of current through thesensing cable to generate N cycles of heating and cooling) can bepropagated through the heating/cooling element 103. The period of aheating/cooling cycle, t₀, the number of heating cycles, N, and thecurrent amplitude. I₀, can be selected. The heating/cooling pulses canbe applied to the heating/cooling element 103 with the excitation source105 to generate thermal excitation within the sensing cable 101.

Temperature readings from the optical fiber sensor array 102 can becollected via the signal interrogator 104 at a selected samplingfrequency. The sampling frequency can be, for example, at least twicethe maximum signal frequency of interest. A temperature series,T_(i)(1), T_(i)(2), T_(i)(3), . . . can be generated where i=1, 2, 3, .. . M, is the sensor index. In accordance with certain embodiments,synchronized sampling techniques can be employed to reduce the samplenumber, increase the signal to noise ratio, and improve Fouriertransform accuracy. The time difference of the temperature readingsΔT=[T(k+1)−T(k)]/Δt, can be calculated using the control unit 106 togenerate time series of temperature derivative ΔT_(i)(1), ΔT_(i)(2),ΔT_(i)(3) . . . , where sensor index i=1, 2, 3 . . . M. In connectionwith the following description, the temperature difference, differencedtemperature, or temperature derivatives are all referred to as the timeseries ΔT′. A transform (e.g., a Fast Fourier Transform [FFT], orDiscrete Fourier Transform [DFT]) can be applied, using the control unit106, to generate a spectrum of time series of temperature difference forM sensors. For each sensor, the real and imaginary values of thespectrum at fundamental frequency of N-Pulse train can be selectedf₀=1/t₀. The characteristics of the surrounding media can thus bedetermined as disclosed herein using M pairs of the values derived fromthe spectrum of the temperature difference as described above.Alternatively, the frequency differenced spectrum (i.e., obtained byapplying the operation of taking the derivative of the spectrum oftemperature difference with respect to the frequency) and the real andimaginary values of the differenced spectrum can be used. Thecharacteristics of the surrounding media can thus be determined asdisclosed herein using M pairs of the values derived from thedifferenced spectrum as described above.

That is, for example, the time derivative of the temperature data can bedetermined (i.e., resulting in the differenced temperature). The Fouriertransform of the time-derivative temperature can then be determined, andthe derivative of the complex spectrum with respect to the frequency canbe calculated (i.e., resulting in the differenced spectrum). Theamplitude and phase of the frequency-derivative spectrum (differencedspectrum) can then be calculated. The amplitude and phase of thefrequency-derivative spectrum can correspond to the characteristics ofthe surrounding media at each sensor location. For purpose ofillustration, FIG. 5B shows the phase of the frequency-derivativespectrum of the temperature measurements over the sensor locations asillustrated in FIG. 3. Likewise, FIG. 5C shows the amplitude of thefrequency-derivative spectrum of the temperature measurements over thesensor locations as illustrated in FIG. 3. As illustrated by thefigures, the techniques disclosed herein can provide for enhancedaccuracy in the measurement and differentiation of the levels andinterfaces between the air, oil, emulsion, and water layers.

As embodied herein, the sensing cable 101 can be calibrated, e.g., withthe control unit 106. Calibration can include calibrating the sensorarray to ensure that each sensor at a different location along thesensing cable provides the same output when subject to the same materialof a constant thermal property. For example, the sensing cable 101 canbe submerged into a homogenous medium of known thermal property, and thetemperature measurements and processing techniques disclosed herein canbe applied. If there is a difference between sensor output, thedifference can be used as compensation and can be applied duringmeasurements. Additionally, calibration can include ensuring that thesensor output accurately estimates the particular characteristic ofinterest (e.g. thermal conductivity and/or diffusivity). For example, anumber of materials with known thermal properties can be measured for abroad range of values and a database can be constructed includingcorrelations between measurements and determined characteristics of theknown materials. The database can then be used to interpolate a measuredcharacteristic of an unknown material.

For purpose of illustration, and not limitation, the underlying theoryof measurement techniques in accordance with this exemplary embodimentwill be described. In connection with this description, for purpose ofexample, the waveform of the pulse train propagated through the heatingdevice can be a square shape current, e.g., as illustrated in FIG. 2.The current can be defined mathematically as:

$\begin{matrix}{{{i(t)} = {\sum\limits_{n = 1}^{N}\; {\left\{ {{H\left( {t - {\left( {n - 1} \right)t_{0}}} \right)} - {H\left( {t - {\left( {n - \frac{1}{2}} \right)t_{0}}} \right)}} \right\} I_{0}}}},} & (17)\end{matrix}$

where t₀ is the period, I₀ is the amplitude of the current, and Hdenotes the Heaviside step function defined by:

$\begin{matrix}{{H\left( {x - x_{0}} \right)} = \left\{ {\begin{matrix}0 & {x < x_{0}} \\1 & {x \geq x_{0}}\end{matrix}.} \right.} & (18)\end{matrix}$

The heating rate can thus be given as:

$\begin{matrix}{{{q(t)} = {\sum\limits_{n = 1}^{N}\; {\left\{ {{H\left( {t - {\left( {n - 1} \right)t_{0}}} \right)} - {H\left( {t - {\left( {n - \frac{1}{2}} \right)t_{0}}} \right)}} \right\} q_{0}}}},} & (19)\end{matrix}$

where q₀ is related to the current by equation 5.

Instead of analyzing the temperature in time domain, the temperaturerate, i.e. the derivative of the temperature with respect to time, canbe considered in the frequency domain. The derivative operation, ahigh-pass filtering, can remove the slow-varying trend of thetemperature for easier analysis. The time derivative of the temperatureand heating generation rate can be defined as follows:

$\begin{matrix}{{\overset{.}{T}\left( {r,t} \right)} = \frac{T}{t}} & (20) \\{{\overset{.}{q}(t)} = {\frac{q}{t}.}} & (21)\end{matrix}$

In frequency domain, the counterparts to the temperature and heatinggeneration rate can be complex spectrum functions of S(r, ω) and Ω(ω).For large distances away from the heating element, the thermal diffusionprocess can exhibit the behavior of an attenuated and dispersive wave.The complex spectrum of the change rate of the temperature on thesensing cable's surface can be given as:

$\begin{matrix}{{S\left( {r_{0},\omega} \right)} = {\frac{1}{2\pi \; k}\frac{\Omega (\omega)}{\kappa \; r_{0}}{\frac{H_{0}^{(2)}\left( {\kappa \; r_{0}} \right)}{H_{1}^{(2)}\left( {\kappa \; r_{0}} \right)}.}}} & (22)\end{matrix}$

The contribution of the heating component, Ω at a center frequency of ω,to the change rate of the temperature on the sensing cable's surface canthus be given as:

d{dot over (T)}(r ₀ ,ω,t)=S(r ₀,ω)e ^(jox) dω.  (23)

Integration of above over all frequencies can recover the temperaturerate in time domain. Therefore, S can be used as indicator of themedium. For purpose of illustration, and not limitation, the excitationterm, Ω will now be described in greater detail. From equations 19 and21, the derivative of the heating generation can be given as:

$\begin{matrix}{{\overset{.}{q}(t)} = {\sum\limits_{i = 1}^{N}\; {\left\{ {{\delta \left( {t - {\left( {i - 1} \right)t_{0}}} \right)} - {\delta \left( {t - {\left( {i - \frac{1}{2}} \right)t_{0}}} \right)}} \right\} q_{0}}}} & (24)\end{matrix}$

in time domain, and:

$\begin{matrix}{{\Omega (\omega)} = {{q_{0}\left( {^{{j\omega}\; t_{0}} - ^{j\frac{\omega \; t_{0}}{2}}} \right)}{\sum\limits_{n = 1}^{N}\; ^{j{({n\; \omega \; t_{0}})}}}}} & (25)\end{matrix}$

in frequency domain. Because N is finite, Ω can contain all frequencies.The components at the harmonic frequencies can be given as:

$\begin{matrix}{{\omega_{k} = {{k\; \omega_{0}} = {k\frac{2\pi}{t_{0}}}}},} & (26)\end{matrix}$

with index k.

Evaluation of equation 25 at the harmonic frequencies gives:

$\begin{matrix}{{\Omega \left( \omega_{k} \right)} = \left\{ {\begin{matrix}{2\; {Nq}_{0}} & {{{k = 1},3,{5\mspace{14mu} \ldots}}\mspace{14mu}} \\0 & {{k = 0},{24\mspace{14mu} \ldots}}\end{matrix}.} \right.} & (27)\end{matrix}$

As such, Ω peaks at odd harmonics but zeros at even harmonics. Atnon-harmonic frequencies, Ω is complex in general. FIG. 5A depicts anexemplary plot of Ω/q₀ verse ω/ω₀ for N=1, 2, or 3. Accordingly, thethermal excitation energy can be concentrated at odd harmonics offundamental frequency of pulses and increase as N increases.

As embodied herein, one of the odd harmonic frequencies can be chosen toincrease signal to noise ratio in analysis of temperature measurements.In this manner, any temperature variation introduced by non-electricalheating can introduce noise which could be difficult to handle in timedomain but can be reduced in frequency domain via N-pulse train: thenumber of cycles, N, can be increased to boost the peak value at oddharmonics. Additionally or alternatively, synchronized samplingtechniques or harmonic tracking can also be used to reduce the noise.

In accordance with an exemplary embodiment, the spectrum S(ω), e.g., asgiven in equation 22, can be used to estimate the thermal property of amedium surrounding the sensing cable. A characteristic frequency can begiven as:

$\begin{matrix}{w^{*} = {\frac{\alpha}{r_{0}^{2}}.}} & (28)\end{matrix}$

The complex argument to the Hankel functions can thus become:

$\begin{matrix}{{{\kappa \; r_{0}} = {{\sqrt{{- j}\frac{\omega}{\alpha}}r_{0}} = {\sqrt{\frac{\omega}{\omega^{*}}}^{j\theta}}}},} & (29)\end{matrix}$

Where θ= 3/4π for ω>0. At low frequencies where ω/ω*(amplitude of κr₀)is less than 1, the Hankel functions can be approximated as:

$\begin{matrix}{{{H_{0}^{(2)}\left( {\kappa \; r_{0}} \right)} \approx {1 - \frac{\left( {\kappa \; r_{0}} \right)^{2}}{4} - {j\frac{\pi}{2}{\ln \left( {\kappa \; r_{0}} \right)}}}}{and}} & (30) \\{{H_{1}^{(2)}\left( {\kappa \; r_{0}} \right)} \approx {\frac{\kappa \; r_{0}}{2} - \frac{\left( {\kappa \; r_{0}} \right)^{3}}{16} + {j\frac{2}{\pi}{\frac{1}{\left( {\kappa \; r_{0}} \right)}.}}}} & (31)\end{matrix}$

The spectrum, S, can thus reduce to:

$\begin{matrix}{{{S\left( {r_{0},\omega} \right)} = {\frac{\Omega}{2\pi \; k}{\hat{X}\left( \frac{\omega}{\omega^{*}} \right)}}},} & (32)\end{matrix}$

where the normalized transfer function, and temperature change responseto the thermal excitation Ω/2πk at frequency ω/ω* can be given as:

$\begin{matrix}{{{\hat{X}\left( \frac{\omega}{\omega^{*}} \right)} = {\left( {R_{s} + {j\; I_{s}}} \right) = {X\; ^{j\varphi}}}},} & (33) \\{{R_{s} \approx \frac{{\frac{1}{32}\left( \frac{\omega}{\omega^{*}} \right)^{2}} + {\frac{1}{2\pi}\frac{\omega}{\omega^{*}}} + {\frac{1}{2\pi}\left( {\frac{\omega}{\omega^{*}} - \frac{4}{\pi}} \right){\ln \left( \frac{\omega}{\omega^{*}} \right)}}}{{\frac{1}{4}\left( \frac{\omega}{\omega^{*}} \right)^{2}} - {\frac{2}{\pi}\left( \frac{\omega}{\omega^{*}} \right)} + \frac{4}{\pi^{2}}}},{and}} & (34) \\{{I_{s} \approx \frac{{\frac{5}{4}\left( {\frac{\omega}{\omega^{*}} - \frac{4}{\pi}} \right)} - {\frac{1}{16\pi}\left( \frac{\omega}{\omega^{*}} \right)^{2}{\ln \left( \frac{\omega}{\omega^{*}} \right)}}}{{\frac{1}{4}\left( \frac{\omega}{\omega^{*}} \right)^{2}} - {\frac{2}{\pi}\left( \frac{\omega}{\omega^{*}} \right)} + \frac{4}{\pi^{2}}}},} & (35)\end{matrix}$

after neglecting terms of higher order.As disclosed herein, and in accordance with an exemplary embodiment ofthe disclosed subject matter, the amplitude and phase can decreasemonotonically with frequency so that higher frequency corresponds withlower response of temperature to the heating. Accordingly, lowerfrequencies can obtain significant heating response and higher signals.Additionally, the imaginary part of the complex spectrum can be nearlylinear with the frequency while the real part can exhibit linearbehavior beyond certain frequency values. Therefore, the derivative ofthe transfer function spectrum with respect to frequency can lead toconstants beyond certain values of ω/ω*. One of ordinary skill in theart will appreciate that, mathematically, the spectral derivative isequivalent to the Fourier transform of the temperature rate with respectto the log of time. Thus there is connection of the derivative spectrumwith the linear relationship of the temperature change with log(t) inthe time domain as shown in equation 13.

As embodied herein, systems and methods in accordance with the disclosedsubject matter include identifying the level of one or more media in avessel with a sensing cable including an optical fiber sensor arrayaligned with a heating/cooling element. The method includes propagatingat least one heating/cooling pulse through the heating/cooling elementalong at least a portion of the sensing cable to affect an exchange ofthermal energy between the heating element and one or more media exposedto the sensing cable. The method includes measuring, over time, atemperature profile of the sensing cable corresponding to the heat pulseat each of a plurality of sensor locations on an optical fiber sensorarray. The method includes identifying a level of each of the one ormore media by determining one or more properties of the one or moremedia exposed to the sensing cable at each of the plurality of sensorlocations based on the temperature profile corresponding thereto.

For purpose of illustration and not limitation, reference is made to theexemplary embodiments of FIG. 1. The method and system disclosed hereincan be used to determine levels in a variety of components and vessels.For example, the vessel can be a desalter unit of a refinery. Inoperation, a desalter unit can typically include some combination ofgas, foam, oil, emulsion, water, and/or solids. Crudes with highasphaltenes, high TAN, high solids, low API gravity, or high viscositycan tend to form emulsions that are difficult to break down. As aresult, water and salt removal can be reduced, the oil content of thebrine can increase, and upsets can become common. Enhanced emulsion banddetection and profiling can help improve level, mix valve, and chemicalinjection control and ultimately can allow partial automation of thedesalter operation. Accordingly, cost-effective solutions for continuousliquid level/interface monitoring (e.g., including monitoring ofinterfaces between solid, water, emulsion, oil, and air) can bedesirable, particularly in connection with desalter applications forchallenged crude.

The level of, and interfaces between, the contents of the desalter unitcan be identified by the system and method herein even under elevatedtemperatures. In another exemplary embodiment, the vessel can be aseparator in a subsea production well. In operation, a subsea productionwell can typically include some combination of natural gas, foam, crude,water, emulsion, and/or sand. Accordingly, the techniques disclosedherein can be employed to identify the level of, and interfaces between,the contents of a separator in a subsea production well. However, it isrecognized that the system and method herein can be applied to numerousother environments and vessels in which the identification of levels andinterfaces is beneficial or desired.

In accordance with this exemplary embodiment, the system for identifyingthe level of one or more media in the vessel can include the componentsand features described herein with reference to FIG. 1A-C. The sensingcable (e.g., sensing cable 101) can further include a shield toestablish an approximately stationary condition of the surrounding mediain a region proximate the sensing cable. As used herein, the term“approximately stationary” can include a static condition, or a flowpattern in which energy transferred from the sensing cable to thesurrounding media is substantially conductive, rather than convective.Such flow conditions can include steady laminar flow, or an area ofturbulent flow (e.g., a plurality of eddies) wherein the mean flowvelocity is approximately stationary. Additionally or alternatively, andas previously described, such a shield can be constructed to protect thesensing cable from damage due to solids in the surrounding media.

For purpose of illustration, and not limitation, FIG. 7 provides aschematic depiction of a shield in accordance with an exemplaryembodiment of the disclosed subject matter. With reference to FIG. 7,the shield 710 can have a semicircular or other suitable shape and canbe disposed upstream of the sensing cable 101 to protect and eliminateflow conditions immediately adjacent the sensing cable 730. If the mediasurrounding the sensing cable has, for example, a laminar flow 720, theshield 710 can create an approximately stationary region 730 proximatethe sensing cable 101 such that heat transfer due to convection andother anomalies resulting from flow conditions is reduced. Any of avariety of suitable materials of construction for the shield can beused, depending on surrounding environmental conditions, such ascorrosion and fouling resistant metal or ceramic for high temperatureenvironment or polymer for lower temperature environments. The size ofthe shield can be large enough to protect the sensor and reduceturbulent flow around the sensor. One of ordinary skill in the art willappreciate that a variety of other suitable shield configurations arepossible, and the scope of the disclosed subject matter is not intendedto be limited to the exemplary embodiments disclosed herein.

Using the systems and techniques as disclosed, and suitablemodifications as desired, a method of identifying levels and/orinterfaces is provided and disclosed herein with reference to FIG. 1Athrough FIG. 5. For purpose of example, and with reference to FIG. 6,the method of identifying the level and interfaces of media will bedescribed in connection with certain exemplary embodiments, wherein thevessel is a desalter unit. One of ordinary skill in the art willappreciate that the techniques disclosed herein can be applied inconnection with a variety of suitable vessels and media, and thedisclosed subject matter is not intended to be limited to the exemplaryembodiments disclosed herein.

With reference to FIG. 6, the method of sensing the level of orinterface between various media in a desalter unit 600 can includepositioning a sensing cable 101 within the desalter unit. The desalterunit 600 can include various media of different composition and/orphase, each having a different density, such that the media formslayers. For example, the desalter unit 600 can include a layer of water640, a layer of emulsion 630 (e.g., a mixture of oil and water), a layerof oil 620, and a layer of gas 610. One of ordinary skill in the artwill appreciate that, during operation, a desalter unit 600 can includea gas layer, including for example hydrogen, light hydrocarbon gases,and/or inert gases such as nitrogen. For purposes of illustration, andnot limitation, the gas layer of a desalter unit can be represented by“air” in experimental environments. As depicted in the figures and asdescribed in connection with certain examples of the disclosed subjectmatter, the gas layer may be referred to, without limitation, as a layerof air.

As previously noted, the sensing cable 101 includes a heating/coolingelement, such as a heating wire, and an optical fiber sensor array, asdisclosed herein. The optical fiber includes a plurality of sensinglocations along the length of the fiber, such that each sensing locationcorresponds to a height within the desalter unit 600. For example, andas previously noted, the optical fiber can include a plurality ofsensors along its length and/or a single fiber sensor can be movable todefine a plurality of sensor locations. The optical fiber sensor iscoupled to an optical signal interrogator 104 to process an opticalsignal therein to obtain temperature measurements at each of the sensorlocations. The optical signal interrogator 104 can further be coupled toa control unit to process the temperature measurements.

As previously described herein, the heating wire is coupled to anexcitation source adapted to propagate electromagnetic waves (e.g.,current 210) through the heating wire, thereby creating correspondingheat pulses (e.g., heat pulse 220). As the heat pulses propagate throughthe heating wire, heat is exchanged between the heating wire, thesensing cable, and the surrounding media at each sensor location. Thetemperature at each sensor location can be recorded, e.g., via theoptical signal interrogator and control unit, to generate a temperatureprofile for each sensor location. For example, temperature can bemeasured as a function of time at each sensor location along the opticalfiber. The temperature profile at each sensor location generally willcorrespond to the characteristics of the medium surrounding the sensingcable at that sensor location. In this manner, for purpose ofillustration, sensor locations that are exposed to gas 610 can result intemperature profiles schematically depicted by graph 611. Sensorlocations exposed to oil 620, emulsion 630, and water 640 can result indifferent temperature profiles 621, 631, and 641, respectively.

The temperature profile (i.e., the temperature as a function of time ata sensor location) can generally exhibit an increase in temperaturecoinciding with the exposure to the heat pulse at the correspondingsensor location. For purpose of illustration, and not limitation, andwith reference to the laws of thermodynamics, the temperature willgenerally increase over the duration of the heat pulse at a ratecorresponding to the characteristics of the surrounding media, andthereafter decrease as the heat from the heat pulse diffuses into thesurrounding media at a rate corresponding to the characteristics of thesurrounding media. Thus, the temperature profiles for each sensorlocation can correspond to the characteristics of the surrounding media,e.g., via the heat capacity of the particular media. For example, andnot limitation, at a sensing location exposed to a gas 610, such as air,the heat transfer from the heating wire into the surrounding air 610 canbe relatively low due to the low heat capacity and conductance of air,which would result in a temperature profile such as that of 611. Bycontrast, at a sensing location exposed to water 640, the heat transferfrom the heating wire into the surrounding water 640 can be relativelyhigh due to the relatively higher heat capacity and conductance ofwater, and thus the temperature profile may resemble that of 641.

As disclosed herein, the control unit thus can be adapted to determinethe characteristics of the surrounding media at each sensor locationusing a variety of techniques, and thereby determine the level orinterfaces between layers of the media in the desalter unit. Forexample, the control unit can be adapted to determine, with reference tothe known positions of the sensor locations and the correspondingtemperature profiles, a difference in characteristics of the mediumsurrounding each sensor location and thus determine the interface orlevel of each medium. In like manner, interfaces between layers can bedetected by identifying a change in temperature profile between sensorlocations.

For purpose of illustration, and not limitation, the direct temperaturemeasurement techniques described above can be used to determine thelevels and/or interfaces between media in a desalter unit. Particularly,and with reference to FIG. 3, a feature temperature profile (e.g.,including three temperature measurements corresponding to a heatingperiod, a peak temperature measurement, and a cooling period) can beextracted and processed to determine characteristics of the mediumsurrounding each sensor location. For example, and as depicted in FIG.3, the temperature profile of sensors exposed to air can have arelatively higher peak, heating, and cooling temperature relative to thetemperature profile of sensors exposed to oil, emulsion, and water.

Alternatively, and as described herein with reference to FIG. 4B, alog-time regression technique can be used to determine thecharacteristics of the medium surrounds each sensor location by furtherprocessing the temperature profile at each sensor location. That is, byperforming the regression of the temperature over log of time over aninterval of time corresponding to each heat pulse for each sensorlocation, the resulting slope and intercept of the regression can beused to identify the characteristics of the medium. For example, and asshown in FIG. 4B, the slope and intercept of sensor locations exposed toair can be relatively high and relatively low, respectively. Bycontrast, the slope and intercept of sensor locations exposed to oil canbe relatively low and high, respectively, relative to air. In likemanner, the slope and intercept of sensor locations exposed to water canbe lower and higher, respectively, than those of oil.

In accordance with another exemplary embodiment of the disclosed subjectmatter, the frequency spectrum techniques disclosed herein withreference to FIG. 5A-C can be employed to determine the level and/orinterfaces between media in the desalter unit 600 with increasedmeasurement sensitivity, accuracy, and/or reliability. In this exemplaryembodiment, and as described above, an N-pulse train can be propagatedthrough the heating wire of the sensing cable 101 with pre-selectedparameters, including heating cycle period, t₀, number of heatingcycles, N, and current amplitude, I₀. The parameters can be selectedaccording to the operating characteristics of the desalter unit 600 suchthat the resulting temperature profile can be measured with a desiredsignal-to-noise ratio. For example, a longer heating cycle period orhigher current amplitude can result in higher signal-to-noise ratiorelative to a shorter heating cycle period or lower current amplitude.Likewise, an increase in the number of heating cycles can furtherincrease the signal-to-noise ratio. One of ordinary skill in the artwill appreciate that such parameters can be varied depending upondesired application. For example, if determination of level and/orinterfaces is desired at short time intervals, a shorter heating cyclerperiod and a higher current amplitude can be employed. For purpose ofexample, and not limitation, in connection with a desalter unit 600, theheating cycle period can be approximately several milliseconds toseveral seconds (i.e., the excitation source can be adapted to deliver acurrent pulse at approximately 0.01 Hz to 100 Hz). The current amplitudecan be approximately 1 mA to approximately 1 A. One of ordinary skill inthe art will appreciate that, in accordance with the disclosed subjectmatter, suitable frequency and current amplitude can be determined for aparticular application by routine testing in accordance with knownmethods.

The optical signal interrogator 104 can be adapted to measuretemperatures from the optical fiber at a pre-selected samplingfrequency. In accordance with an exemplary embodiment, the samplingfrequency can be at least twice the expected frequency of thetemperature profile and/or heat pulse. For example, and not limitation,in connection with a desalter unit 600 the sampling frequency can be 50Hz. The derivative with respect to time of the temperature measurementsfor each sensor location can then be generated. For example, themeasured temperatures a sensor location at each sampling interval can begiven as a temperature series. The difference between each temperaturein the series can then be calculated to generate a temperaturederivative series. A transform (e.g., a FFT or DFT) can be applied toconvert the temperature derivative series into the frequency domain, andthus generate a spectrum of time series of temperature differences foreach sensor location. The derivative of the spectrum, with respect tothe frequency, can be generated. That amplitude and phase of thefrequency-derivative spectrum (e.g., the real and imaginary parts of thecomplex frequency-derivative spectrum) can then be determined. Forexample, using the heating cycle period, t₀, the real and imaginaryvalues of the spectrum at the fundamental frequency of the N-pulse traincan be selected at f₀=1/t₀.

The amplitude and phase of the frequency-derivative spectrum at eachsensor location, as depicted in FIG. 5B and FIG. 5C, thus can correspondto a particular medium surrounding the sensing cable 101 at a particularsensor location. For example, the amplitude and phase can decreasemonotonically with frequency so that higher frequency corresponds withlower response to a change in temperature from the heating element.Accordingly, lower frequencies can obtain significant heating responseand higher signals. Additionally, the imaginary part of the complexspectrum can be nearly linear with the frequency while the real part canexhibit linear behavior beyond certain frequency values. Therefore, thederivative of the transfer function spectrum with respect to frequencycan correspond to the linear relationship of the temperature change withlog(t) in the time domain. In this manner, and as depicted in FIG. 5Band FIG. 5C, the amplitude and phase of sensor locations exposed to aircan be relatively high as compared to the amplitude and phase of sensorlocations exposed to oil, emulsion, or water. The amplitude and phase ofsensor locations exposed to oil can be lower than the amplitude andphase of air and can be higher than the amplitude and phase of water.The phase of sensor locations exposed to emulsion can be relatively highas compared to the phase of sensor locations exposed to oil and waterand relatively low as compared to the phase of sensor locations exposedto air. The amplitude of sensor locations exposed to emulsion can be lowas compared to the amplitude of sensor locations exposed to air, and canbe high as compared to the amplitude of sensor locations exposed towater.

The sensing cable 101 can be calibrated, e.g., with the control unit.Calibration can include, for example, calibrating the sensor array todetermine the amplitude and phase of the frequency-derivative spectrumof certain known media. For example, a number of materials with knownthermal properties can be measured for a broad range of values and adatabase can be constructed including correlations between the generatedamplitude and phase and characteristics of the known materials. Thedatabase can then be used as to determine the surrounding medium at aparticular sensor location in the desalter unit 600.

The control unit, with reference to the known locations of each sensorand the corresponding amplitude and phase of the frequency-derivativespectrum, can determine the level and/or interface between layers (610,620, 630, 640) of different media in the desalter unit 600. To determinethe level of the various layers, the control unit can be configured tostore the known position of each sensor location in one or morememories. For example, for a 36 inch tall desalter unit with a sensingcable having 36 sensor locations, each spaced apart by a unit inch, thecontrol unit can store the height value of each sensor location (i.e.,for sensor location i={1, 2, . . . , 36}, the control unit can store acorresponding height measurement H_(i)={1 in, 2 in, . . . , 36 in}). Foreach sensor location, i, the control unit can determine the amplitudeand phase of the frequency derivative spectrum as disclosed herein. Withreference to, for example, a database storing the amplitude and phase ofthe frequency derivative spectrum for known media, the control unit canthus determine which medium surrounds each sensor location using thedetermined amplitude and phase at each sensor location.

Additionally or alternatively, as embodied herein, the control unit canprocess the determined amplitude or phase of the frequency derivativespectrum of adjacent sensor locations to determine the location ofinterfaces between various layers in the desalter 600. That is, forexample, a change in the amplitude across two sensor locations, asillustrated in FIG. 5C, can correspond to an interface between thosesensors. Likewise, a change in the phase, as illustrated in FIG. 5B, cancorrespond to an interface. In certain embodiments, the control unit canprocess both the amplitude and phase of adjacent sensors to enhancedetection of interfaces. For example, a change in both the amplitude andphase can correspond to an interface.

The methods disclosed herein can provide for continuous profilemonitoring in real time, and multiple liquid levels or interfaces can bemeasured and visualized simultaneously. No moving mechanical parts needbe included inside the sensing cable. Because material thermalproperties can be measured for level/interface sensing, the measurementresults can be independent of electrical conductivity, salinity, andcrude oil constituents, such as sulfur, iron sulfide/oxide. Moreover,relative temperature changes before and after heating/cooling can beused to infer material thermal properties for level/interfacemeasurement, and temperature baseline can be taken each time beforeheating/cooling is applied. Accordingly, the techniques disclosed hereinneed not require long term stability for temperature sensors.

Moreover, the system disclosed herein can operate at temperaturesranging from cryogenic temperatures up to over 1000° C. The size of thesensing cable can be relatively small (e.g., compared to conventionalthermocouples) and can be cost effective for large area coverage with alarge amount of sensors. Utilizing cost-effective optical fibertemperature sensors, the system disclosed herein can incorporate a largenumber of sensors, and can offer a high spatial resolution, e.g., lessthan 1 mm, over a long measurement range, e.g. several meters tokilometers. The diameter of the compact sensing cable can small, e.g.,less than 2 mm. The small diameter of the sensing cable can allow formeasurement in a tight space with reduced intrusiveness. The techniquesdisclosed herein can be used, for example, in connection with qualitycontrol in liquid/liquid extraction processes, and/or the monitoring ofliquid properties, such as the presence of water and gas, and water andgas entrance in production wells. In addition, the system disclosedherein can be used to optimize the gas lift by monitoring the bubbleconditions along the well.

Additional Embodiments

Additionally or alternately, the invention can include one or more ofthe following embodiments.

Embodiment 1

A method for identifying the level of one or more media in a vessel,comprising: providing within a vessel a sensing cable including anoptical fiber sensor array aligned with a heating element; propagatingat least one heat pulse through the heating element along at least aportion of the sensing cable to affect an exchange of thermal energybetween the heating element and the one or more media exposed to thesensing cable; measuring, over time, a temperature profile of thesensing cable corresponding to the heat pulse at each of a plurality ofsensor locations on the optical fiber sensor array; and identifying alevel of each of the one or more media by determining one or moreproperties of the one or more media exposed to the sensing cable at eachof the plurality of sensor locations based on the temperature profilecorresponding thereto.

Embodiment 2

the method of any one of the previous embodiments, wherein the vesselincludes a desalter unit, and wherein identifying the level of one ormore media includes identifying the level of one or more of gas, foam,oil, emulsion, water, or solids.

Embodiment 3

the method of any one of the previous embodiments, wherein the vesselincludes a subsea production well, and wherein identifying the level ofone or more media includes identifying the level of one or more of gas,foam, crude, water, emulsion, or sand.

Embodiment 4

the method of any one of the previous embodiments, wherein the at leastone heat pulse further includes a plurality of heat pulses.

Embodiment 5

the method of any one of the previous embodiments, wherein measuring,over time, the temperature profile includes measuring using fiber Bragggrating array based sensing, Raman scattering based sensing. Rayleighscattering based sensing, or Brillioun scattering based sensing.

Embodiment 6

the method of any one of the previous embodiments, wherein the heatingelement includes a resistive heating element and wherein propagating theat least one heat pulse includes applying an electrical pulse with apredetermined frequency and predetermined waveform.

Embodiment 7

the method of any one of the previous embodiments, wherein propagatingat least one heat pulse through the heating element includes propagatingthe at least one heat pulse through a heating element aligned adjacentto the optical fiber sensor array.

Embodiment 8

the method of embodiments, 1, 2, 3, 4, 5 or 6, wherein propagating atleast one heat pulse through the heating element includes propagatingthe at least one heat pulse through a heating element disposedconcentrically with the optical fiber sensor array.

Embodiment 9

the method of embodiments 1, 2, 3, 4, 5, 7 or 8, wherein the heatingelement includes a thermoelectric device and wherein propagating atleast one heat pulse through the heating element includes propagatingcooling pulse.

Embodiment 10

the method of any one of the previous embodiments, further comprisingcoating the sensing cable with an anti-fouling coating to preventformation of deposits thereon.

Embodiment 11

the method of any one of the previous embodiments, further comprisingshielding the sensing cable to attenuate flow of the one or more mediaimmediately exposed to the sensing cable.

Embodiment 12

the method of any one of the previous embodiments, wherein measuring thetemperature profile corresponding to the heat pulse at each of theplurality of sensor locations includes, for each sensor location,measuring at least a heating temperature measurement during propagationof the heat pulse over the sensor location, a peak temperaturemeasurement, and a cooling temperature measurement after propagation ofthe heat pulse over the sensor.

Embodiment 13

the method of embodiment 12, wherein identifying the level of the one ormore media includes calculating a difference in the heating temperaturemeasurement, the peak temperature measurement, the cooling temperaturemeasurement, or combination thereof, between adjacent sensor locations,wherein the difference indicates an interface between two of the one ormore media if the difference exceeds a predetermined threshold.

Embodiment 14

the method of any one of the previous embodiments, wherein measuring thetemperature profile corresponding to the heat pulse at each of theplurality of sensor locations includes, for each sensor location,measuring a plurality of temperatures over a period of time upon arrivalof the heat pulse at the sensor location.

Embodiment 15

the method of embodiment 14, wherein identifying the level of the one ormore media includes, for each temperature profile, performing aregression of the plurality of temperatures over a logarithm ofcorresponding measurement times for a predetermined time window in theperiod of time to generate a slope and an intercept of the regression,wherein the slope and the intercept relate to the one or more propertiesof the medium exposed to the sensing cable at the sensor location.

Embodiment 16

the method of embodiment 15, wherein the predetermined time windowincludes a time window during a heating stage, the heating stagecorresponding to a period of time during propagation of the heat pulseover the sensor location or a time window during a cooling stage, thecooling stage corresponding to a period of time after propagation of theheat pulse over the sensor.

Embodiment 17

the method of embodiment 15 or 16, wherein identifying the level of theone or more media further includes calculating a difference in the slopeand the intercept between adjacent sensor locations, wherein thedifference indicates an interface between two of the one or more mediaif the difference exceeds a predetermined threshold.

Embodiment 18

the method of embodiment 14, 15, 16 or 17 wherein identifying the levelof the one or more media includes, for each temperature profile:generating a time derivative by calculating a derivative of theplurality of temperature measurements with respect to time, applying atransform to the time derivative to generate a complex spectrum; anddetermining an amplitude and a phase of the complex spectrum, whereinthe amplitude and the phase of the complex spectrum relate to the one ormore properties of the medium exposed to the sensing cable at the sensorlocation.

Embodiment 19

the method of embodiment 18, wherein identifying the level of the one ormore media further includes, for each temperature profile: generating afrequency derivative spectrum by calculating the derivative of thecomplex spectrum with respect to frequency; and determining an amplitudeand a phase of the frequency derivative spectrum, wherein the amplitudeand the phase of the frequency derivative spectrum relate to the one ormore properties of the medium exposed to the sensing cable at the sensorlocation.

Embodiment 20

the method of embodiment 18 or 19, wherein identifying the level of theone or more media further includes calculating a difference in theamplitude and the phase between adjacent sensor locations, wherein thedifference indicates an interface between two of the one or more mediaif the difference exceeds a predetermined threshold.

Embodiment 21

the method of any one of the previous embodiments, wherein the vesselhas an operating temperature between cryogenic temperatures andapproximately 1000° C., wherein the sensing cable has a diameter of lessthan 2 mm, and wherein the optical signal interrogator is configured tomeasure the temperature profile at a spatial resolution less than 1 mm.

Embodiment 22

A system for identifying the level of one or more media in a vesselincluding one or more media, comprising: a sensing cable including anoptical fiber sensor array aligned with a heating element disposed inthe vessel, the optical fiber sensor array having a plurality of sensorlocations; an excitation source coupled with the heating element andconfigured to propagate at least one heat pulse through the heatingelement along at least a portion of the sensing cable to affect anexchange of thermal energy between the heating element and the one ormore media exposed to the sensing cable; an optical signal interrogatorcoupled with the optical fiber sensor array and adapted to receive asignal from each of the plurality of sensor locations and configured tomeasure, over time, a temperature profile of the sensing cablecorresponding to the heat pulse at each of the plurality of sensorlocations on the optical fiber sensor array; and a control unit, coupledwith the heating element and the optical signal interrogator, toidentify a level of each of the one or more media by determining one ormore properties of the one or more media exposed to the sensing cable ateach of the plurality of sensor locations based on the temperatureprofile corresponding thereto.

Embodiment 23

the system of embodiment 22, wherein the vessel includes a desalterunit, and wherein the one or more media include one or more of gas,foam, oil, emulsion, water, or solids.

Embodiment 24

the system of embodiments 22 or 23, wherein the vessel includes a subseaproduction well, and wherein the one or more media include one or moreof gas, foam, crude, water, emulsion, or sand.

Embodiment 25

the system of embodiments 22, 23, or 24, where the excitation source iffurther configured to propagate a plurality of heat pulses through theheating element.

Embodiment 26

the system of embodiments 22, 23, 24, or 25, wherein the optical fibersensor array and the optical signal interrogator include a fiber Bragggrating array based sensing system, a Raman scattering based sensingsystem, a Rayleigh scattering based sensing system, or a Brilliounscattering based sensing system.

Embodiment 27

the system of embodiments 22, 23, 24, 25, or 26, wherein the heatingelement includes a resistive heating element and wherein the excitationsource is configured to propagate an electrical pulse with apredetermined frequency and predetermined waveform, the electrical pulsecorresponding to the at least one heat pulse.

Embodiment 28

the system of embodiments 22, 23, 24, 25, 26 or 27, wherein the heatingelement is aligned adjacent to the optical fiber sensor array.

Embodiment 29

the system of embodiments 22, 23, 24, 25, 26 or 27, wherein the heatingelement is disposed concentrically with the optical fiber sensor array.

Embodiment 30

the system of embodiments 22, 23, 24, 25, 26, 28 or 29, wherein theheating element includes a thermoelectric device and wherein the atleast one heat pulse includes a cooling pulse.

Embodiment 31

the system of embodiments 22, 23, 24, 25, 26, 27, 28, 29 or 30, whereinthe sensing cable further includes an anti-fouling coating to preventformation of deposits thereon.

Embodiment 32

the system of embodiments 22, 23, 24, 25, 26, 27, 28, 29, 30 or 31,wherein the sensing cable further includes a shield to attenuate flow ofthe one or more media immediately exposed to the sensing cable.

Embodiment 33

the system of embodiments 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, or 32,wherein the optical signal interrogator is configured, for each of theplurality of sensor locations, to measure at least a heating temperaturemeasurement during propagation of the heat pulse over the sensorlocation, a peak temperature measurement, and a cooling temperaturemeasurement after propagation of the heat pulse over the sensor.

Embodiment 34

the system of embodiment 33, wherein the control unit is configured tocalculate a difference in the heating temperature measurement, the peaktemperature measurement, the cooling temperature measurement, orcombination thereof between adjacent sensor locations, wherein thedifference indicates an interface between two of the one or more mediaif the difference exceeds a predetermined threshold.

Embodiment 35

the system of embodiments 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33or 34 wherein the optical signal interrogator is configured, for each ofthe plurality of sensor locations, to measure a plurality oftemperatures over a period of time upon arrival of the heat pulse at thesensor location.

Embodiment 36

the system of embodiment 35, wherein the control unit is configured, foreach temperature profile, to perform a regression of the plurality oftemperatures over a logarithm of corresponding measurement times for apredetermined time window in the period of time to generate a slope andan intercept of the regression, wherein the slope and the interceptrelate to the one or more properties of the medium exposed to thesensing cable at the sensor location.

Embodiment 37

the system of embodiment 36, wherein the predetermined time windowincludes a time window during a heating stage, the heating stagecorresponding to a period of time during propagation of the heat pulseover the sensor location or a time window during a cooling stage, thecooling stage corresponding to a period of time after propagation of theheat pulse over the sensor.

Embodiment 38

the system of embodiments 36 or 37, wherein the control unit isconfigured to calculate a difference in the slope and the interceptbetween adjacent sensor locations, wherein the difference indicates aninterface between two of the one or more media if the difference exceedsa predetermined threshold.

Embodiment 39

the system of embodiments 35, 36, 37, or 38, wherein the control unit isconfigured, for each temperature profile, to: generate a time derivativeby calculating a derivative of the plurality of temperature measurementswith respect to time; apply a transform to the time derivative togenerate a complex spectrum; and determine an amplitude and a phase ofthe complex spectrum, wherein the amplitude and the phase of the complexspectrum relate to the one or more properties of the medium exposed tothe sensing cable at the sensor location.

Embodiment 40

the system of embodiment 39, wherein the control unit is furtherconfigured, for each temperature profile, to: generate a frequencyderivative spectrum by calculating the derivative of the complexspectrum with respect to frequency; and determine an amplitude and aphase of the frequency derivative spectrum, wherein the amplitude andthe phase of the frequency derivative spectrum relate to the one or moreproperties of the medium exposed to the sensing cable at the sensorlocation.

Embodiment 41

the system of embodiments 39 or 40, wherein the control unit isconfigured calculate a difference in the amplitude and the phase betweenadjacent sensor locations, wherein the difference indicates an interfacebetween two of the one or more media if the difference exceeds apredetermined threshold.

Embodiment 42

the system of embodiments 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32,33, 34, 35, 36, 37, 38, 39, 40 or 41, wherein the vessel has anoperating temperature between cryogenic temperatures and approximately1000° C., wherein the sensing cable has a diameter of less than 2 mm,and wherein the optical signal interrogator is configured to measure thetemperature profile at a spatial resolution less than 1 mm.

While the disclosed subject matter is described herein in terms ofcertain exemplary embodiments, those skilled in the art will recognizethat various modifications and improvements can be made to the disclosedsubject matter without departing from the scope thereof. Moreover,although individual features of one embodiment of the disclosed subjectmatter can be discussed herein or shown in the drawings of the oneembodiment and not in other embodiments, it should be apparent thatindividual features of one embodiment can be combined with one or morefeatures of another embodiment or features from a plurality ofembodiments.

In addition to the specific embodiments claimed below, the disclosedsubject matter is also directed to other embodiments having any otherpossible combination of the dependent features claimed below and thosedisclosed above. As such, the particular features presented in thedependent claims and disclosed above can be combined with each other inother manners within the scope of the disclosed subject matter such thatthe disclosed subject matter should be recognized as also specificallydirected to other embodiments having any other possible combinations.Thus, the foregoing description of specific embodiments of the disclosedsubject matter has been presented for purposes of illustration anddescription. It is not intended to be exhaustive or to limit thedisclosed subject matter to those embodiments disclosed.

It will be apparent to those skilled in the art that variousmodifications and variations can be made in the method and system of thedisclosed subject matter without departing from the spirit or scope ofthe disclosed subject matter. Thus, it is intended that the disclosedsubject matter include modifications and variations that are within thescope of the appended claims and their equivalents.

What is claimed is:
 1. A method for identifying the level of one or moremedia in a vessel, comprising: providing within a vessel a sensing cableincluding an optical fiber sensor array aligned with a heating element,propagating at least one heat pulse through the heating element along atleast a portion of the sensing cable to affect an exchange of thermalenergy between the heating element and the one or more media exposed tothe sensing cable; measuring, over time, a temperature profile of thesensing cable corresponding to the heat pulse at each of a plurality ofsensor locations on the optical fiber sensor array; and identifying alevel of each of the one or more media by determining one or moreproperties of the one or more media exposed to the sensing cable at eachof the plurality of sensor locations based on the temperature profilecorresponding thereto.
 2. The method of claim 1, wherein the vesselincludes a desalter unit, and wherein identifying the level of one ormore media includes identifying the level of one or more of gas, foam,oil, emulsion, water, or solids.
 3. The method of claim 1, wherein thevessel includes a subsea production well, and wherein identifying thelevel of one or more media includes identifying the level of one or moreof gas, foam, crude, water, emulsion, or sand.
 4. The method of claim 1,wherein the at least one heat pulse further includes a plurality of heatpulses.
 5. The method of claim 1, wherein measuring, over time, thetemperature profile includes measuring using fiber Bragg grating arraybased sensing, Raman scattering based sensing, Rayleigh scattering basedsensing, or Brillioun scattering based sensing.
 6. The method of claim1, wherein the heating element includes a resistive heating element andwherein propagating the at least one heat pulse includes applying anelectrical pulse with a predetermined frequency and predeterminedwaveform.
 7. The method of claim 1, wherein propagating at least oneheat pulse through the heating element includes propagating the at leastone heat pulse through a heating element aligned adjacent to the opticalfiber sensor array.
 8. The method of claim 1, wherein propagating atleast one heat pulse through the heating element includes propagatingthe at least one heat pulse through a heating element disposedconcentrically with the optical fiber sensor array.
 9. The method ofclaim 1, wherein the heating element includes a thermoelectric deviceand wherein propagating at least one heat pulse through the heatingelement includes propagating cooling pulse.
 10. The method of claim 1,further comprising coating the sensing cable with an anti-foulingcoating to prevent formation of deposits thereon.
 11. The method ofclaim 1, further comprising shielding the sensing cable to attenuateflow of the one or more media immediately exposed to the sensing cable.12. The method of claim 1, wherein measuring the temperature profilecorresponding to the heat pulse at each of the plurality of sensorlocations includes, for each sensor location, measuring at least aheating temperature measurement during propagation of the heat pulseover the sensor location, a peak temperature measurement, and a coolingtemperature measurement after propagation of the heat pulse over thesensor.
 13. The method of claim 12, wherein identifying the level of theone or more media includes calculating a difference in the heatingtemperature measurement, the peak temperature measurement, the coolingtemperature measurement, or combination thereof, between adjacent sensorlocations, wherein the difference indicates an interface between two ofthe one or more media if the difference exceeds a predeterminedthreshold.
 14. The method of claim 1, wherein measuring the temperatureprofile corresponding to the heat pulse at each of the plurality ofsensor locations includes, for each sensor location, measuring aplurality of temperatures over a period of time upon arrival of the heatpulse at the sensor location.
 15. The method of claim 14, whereinidentifying the level of the one or more media includes, for eachtemperature profile, performing a regression of the plurality oftemperatures over a logarithm of corresponding measurement times for apredetermined time window in the period of time to generate a slope andan intercept of the regression, wherein the slope and the interceptrelate to the one or more properties of the medium exposed to thesensing cable at the sensor location.
 16. The method of claim 15,wherein the predetermined time window includes a time window during aheating stage, the heating stage corresponding to a period of timeduring propagation of the heat pulse over the sensor location or a timewindow during a cooling stage, the cooling stage corresponding to aperiod of time after propagation of the heat pulse over the sensor. 17.The method of claim 15, wherein identifying the level of the one or moremedia further includes calculating a difference in the slope and theintercept between adjacent sensor locations, wherein the differenceindicates an interface between two of the one or more media if thedifference exceeds a predetermined threshold.
 18. The method of claim14, wherein identifying the level of the one or more media includes, foreach temperature profile: generating a time derivative by calculating aderivative of the plurality of temperature measurements with respect totime; applying a transform to the time derivative to generate a complexspectrum; and determining an amplitude and a phase of the complexspectrum, wherein the amplitude and the phase of the complex spectrumrelate to the one or more properties of the medium exposed to thesensing cable at the sensor location.
 19. The method of claim 18,wherein identifying the level of the one or more media further includes,for each temperature profile: generating a frequency derivative spectrumby calculating the derivative of the complex spectrum with respect tofrequency; and determining an amplitude and a phase of the frequencyderivative spectrum, wherein the amplitude and the phase of thefrequency derivative spectrum relate to the one or more properties ofthe medium exposed to the sensing cable at the sensor location.
 20. Themethod of claim 18, wherein identifying the level of the one or moremedia further includes calculating a difference in the amplitude and thephase between adjacent sensor locations, wherein the differenceindicates an interface between two of the one or more media if thedifference exceeds a predetermined threshold.
 21. The method of claim 1,wherein the vessel has an operating temperature between cryogenictemperatures and approximately 1000° C., wherein the sensing cable has adiameter of less than 2 mm, and wherein the optical signal interrogatoris configured to measure the temperature profile at a spatial resolutionless than 1 mm.
 22. A system for identifying the level of one or moremedia in a vessel including one or more media, comprising: a sensingcable including an optical fiber sensor array aligned with a heatingelement disposed in the vessel, the optical fiber sensor array having aplurality of sensor locations; an excitation source coupled with theheating element and configured to propagate at least one heat pulsethrough the heating element along at least a portion of the sensingcable to affect an exchange of thermal energy between the heatingelement and the one or more media exposed to the sensing cable; anoptical signal interrogator coupled with the optical fiber sensor arrayand adapted to receive a signal from each of the plurality of sensorlocations and configured to measure, over time, a temperature profile ofthe sensing cable corresponding to the heat pulse at each of theplurality of sensor locations on the optical fiber sensor array; and acontrol unit, coupled with the heating element and the optical signalinterrogator, to identify a level of each of the one or more media bydetermining one or more properties of the one or more media exposed tothe sensing cable at each of the plurality of sensor locations based onthe temperature profile corresponding thereto.
 23. The system of claim22, wherein the vessel includes a desalter unit, and wherein the one ormore media include one or more of gas, foam, oil, emulsion, water, orsolids.
 24. The system of claim 22, wherein the vessel includes a subseaproduction well, and wherein the one or more media include one or moreof gas, foam, crude, water, emulsion, or sand.
 25. The system of claim22, where the excitation source if further configured to propagate aplurality of heat pulses through the heating element.
 26. The system ofclaim 22, wherein the optical fiber sensor array and the optical signalinterrogator include a fiber Bragg grating array based sensing system, aRaman scattering based sensing system, a Rayleigh scattering basedsensing system, or a Brillioun scattering based sensing system.
 27. Thesystem of claim 22, wherein the heating element includes a resistiveheating element and wherein the excitation source is configured topropagate an electrical pulse with a predetermined frequency andpredetermined waveform, the electrical pulse corresponding to the atleast one heat pulse.
 28. The system of claim 22, wherein the heatingelement is aligned adjacent to the optical fiber sensor array.
 29. Thesystem of claim 22, wherein the heating element is disposedconcentrically with the optical fiber sensor array.
 30. The system ofclaim 22, wherein the heating element includes a thermoelectric deviceand wherein the at least one heat pulse includes a cooling pulse. 31.The system of claim 22, wherein the sensing cable further includes ananti-fouling coating to prevent formation of deposits thereon.
 32. Thesystem of claim 22, wherein the sensing cable further includes a shieldto attenuate flow of the one or more media immediately exposed to thesensing cable.
 33. The system of claim 22, wherein the optical signalinterrogator is configured, for each of the plurality of sensorlocations, to measure at least a heating temperature measurement duringpropagation of the heat pulse over the sensor location, a peaktemperature measurement, and a cooling temperature measurement afterpropagation of the heat pulse over the sensor.
 34. The system of claim33, wherein the control unit is configured to calculate a difference inthe heating temperature measurement, the peak temperature measurement,the cooling temperature measurement, or combination thereof betweenadjacent sensor locations, wherein the difference indicates an interfacebetween two of the one or more media if the difference exceeds apredetermined threshold.
 35. The system of claim 22, wherein the opticalsignal interrogator is configured, for each of the plurality of sensorlocations, to measure a plurality of temperatures over a period of timeupon arrival of the heat pulse at the sensor location.
 36. The system ofclaim 35, wherein the control unit is configured, for each temperatureprofile, to perform a regression of the plurality of temperatures over alogarithm of corresponding measurement times for a predetermined timewindow in the period of time to generate a slope and an intercept of theregression, wherein the slope and the intercept relate to the one ormore properties of the medium exposed to the sensing cable at the sensorlocation.
 37. The system of claim 36, wherein the predetermined timewindow includes a time window during a heating stage, the heating stagecorresponding to a period of time during propagation of the heat pulseover the sensor location or a time window during a cooling stage, thecooling stage corresponding to a period of time after propagation of theheat pulse over the sensor.
 38. The system of claim 36, wherein thecontrol unit is configured to calculate a difference in the slope andthe intercept between adjacent sensor locations, wherein the differenceindicates an interface between two of the one or more media if thedifference exceeds a predetermined threshold.
 39. The system of claim35, wherein the control unit is configured, for each temperatureprofile, to: generate a time derivative by calculating a derivative ofthe plurality of temperature measurements with respect to time; apply atransform to the time derivative to generate a complex spectrum; anddetermine an amplitude and a phase of the complex spectrum, wherein theamplitude and the phase of the complex spectrum relate to the one ormore properties of the medium exposed to the sensing cable at the sensorlocation.
 40. The system of claim 39, wherein the control unit isfurther configured, for each temperature profile, to: generate afrequency derivative spectrum by calculating the derivative of thecomplex spectrum with respect to frequency; and determine an amplitudeand a phase of the frequency derivative spectrum, wherein the amplitudeand the phase of the frequency derivative spectrum relate to the one ormore properties of the medium exposed to the sensing cable at the sensorlocation.
 41. The system of claim 39, wherein the control unit isconfigured calculate a difference in the amplitude and the phase betweenadjacent sensor locations, wherein the difference indicates an interfacebetween two of the one or more media if the difference exceeds apredetermined threshold.
 42. The system of claim 22, wherein the vesselhas an operating temperature between cryogenic temperatures andapproximately 1000° C., wherein the sensing cable has a diameter of lessthan 2 mm, and wherein the optical signal interrogator is configured tomeasure the temperature profile at a spatial resolution less than 1 mm.